In future linear colliders it is essential to have very flat beams at the interaction point (IP) in order to obtain high luminosity. The typical beam size is 3nm() x 260nm() at IP for the Japan Linear Collider (JLC-I). A measurement of the beam size is extremely important from the view point of beam diagnostics, especially to maintain the stable operation of linear colliders. Although several ideas have been presented for this purpose, none of them can be used at IP. Recently, T.Shintake has proposed a nanometer beam-size monitor utilizing backward Compton scattering of interfering laser light, which can be used to measure the beam size down to 5nm. We can not measure with certainty 3nm or smaller size, even with this method. So far, there has been no idea of how to clearly measure such a small beam size, much less to measure it during a collision.
In this paper we describe a completely new idea for measuring the beam size at IP. As is well known, many low-energy pairs are expected to be created during beam crossing due to three incoherent processes: the Breit-Wheeler (BW:) process, the Bethe-Heitler (BH: ) process and the Landau-Lifshitz (LL: ) process, where is a beamstrahlung photon. These phenomena have been investigated as troublesome background for experiments at future linear colliders. The particles of our concern have the same charge as that of the oncoming beam, and are hereafter called ``same-charge" particles. Most of them are deflected at larger angles than their inherent scattering angles by a strong electromagnetic force due to the oncoming beam, while the ``opposite-charge" particles must oscillate inside the oncoming beam because of a focussing force between them; they are deflected with small angles. Figure 1 shows a schematic view of these phenomena.
Figure 1: Schematic view of pair creations and deflections during a collision, where two flat beams are depicted as overlapping sheets at IP and two pairs are created in forward and backward angles, only as an example.
They can be well described by a scattering process of in a two-dimensional Coulomb potential which is Lorentz-boosted to the rest frame of the oncoming beam. Since this potential is produced by the intense electric charge of the oncoming beam, it is a function of the transverse size (,) and intensity of the beam. Therefore, the deflected particles should carry this information, especially in their angular distribution, which we intend to measure. It should be noted that we can measure the sizes of the two beams independently, since the particles must be deflected asymmetrically in the forward and backward angular regions if the two beams have different beam parameters, i.e. there are two independent Coulomb potentials of the two beams separated by a large Lorentz-boost along the beam axis. Moreover, we can measure the relative displacement and transverse rotation of two beams. In addition, this measurement will provide a real-time, fast feedback to collider-machine operation at the same time that experiments are being conducted.
In subsequent sections we describe an analytic expression for the angular distribution of elliptic beams, where the charge density is uniform inside an elliptic cylinder, since only this case can be calculated analytically, and, further, it explains most of the features for Gaussian beams under the beam-beam effects at IP. We then present the results of a simulation using the ABEL program[6, 4], which takes account of all known beam-beam effects, for the case of JLC-I as an example of future linear colliders.